Preheat the oven to 350 and line a loaf pan with parchment paper.
In a large bowl combine the eggs, sugar and oil, stir until well mixed.
Add in the Greek yogurt, grated zucchini, lemon juice, lemon zest and vanilla, mix well.
In a separate bowl, gently whisk together flour, sugar, and baking powder.
Gradually add the flour mixture into the zucchini mixture a little at a time mixing well between each addition.
Pour the batter into the prepared pan and place in the oven for 50-60 minutes or until a toothpick inserted in the center comes out clean.
Place the bread on a wire rack and let the bread cool completely before glazing. You can let the bread cool in the pan until it is cool enough to touch and then lift it out by the parchment paper to cool completely.
While the bread is cooling you can make the glaze.
To make the glaze–
Place the powdered sugar in a bowl and gradually add lemon juice and stir. For a thicker glaze add less lemon juice, for a thinner glaze add more.
Pour the glaze over the bread evenly, and sprinkle with lemon zest if desired.
Slice and serve!